Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

Abstract

The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground state properties are also investigated, the corresponding ground state phase diagram is presented.

Antiferromagnetism and the emergence of frustration in the sawtooth lattice chalcogenide olivines Mn2SiS4−xSex ( xNhalil1, Baral2, Khamala3 et al. 2019Phys. Rev. B101160View full textAdd to dashboardCite

“…The saw-tooth antiferromagnetic chain has a frustrated topology of corner-sharing triangles of spins where the ground state of the spin-half saw-tooth chain is understood exactly [1][2][3] . Variety of ground states are predicted for the saw-tooth lattice depending on the ratio of the exchange interaction strengths between the base-base and the base-vertex pairs [4][5][6][7][8] . The saw-tooth systems attain importance in connection with the zero energy flat-band modes similar to the case of Kagome lattices 9,10 and are valuable as potential materials for magnonics 11 .…”

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

“…(3), the upper panel demonstrates phase diagram for the sawtooth chain with Ising and Heisenberg bond without lattice distortions, which was previously obtained in Ref. [ 35], the lower panel demonstrates effects of biquadratic term originated by lattice distortions. Actually, this term enhances the magnetization plateau at M = 1/2, which corresponds to the ferrimagnetic phase |F 1 .…”

“…Then, the partition function of that type can be calculated exactly [33][34][35] within transfer-matrix formalism. To proceed, one needs to calculate the trace for each block quantum spins, and then to sum over two values of τ i in each block to give Eq.…”

“…Despite great successes in exact describing of thermodynamic functions for integrable models by TBA and especially by QTM 25,26 , for many other physically and principally important low-dimensional strongly correlated lattice models only laborious numerical calculations provide more or less reliable results for finite T thermodynamics. Recently, many papers have been devoted to exact solution of the low-dimensional lattice spin models with mixed Ising and Heisenberg bonds [27][28][29][30][31][32][33][34][35][36][37] or just to pure Ising counterparts of known Heisenberg models with various one-dimensional topologies of bonds [38][39][40][41][42] . These exact solutions for modified models have much in common with the numerical and experimental results obtained for their Heisenberg counterparts.…”

“…[27] as the model of magnetic structure of the compound Cu(3-Clpy) 2 (N 3 ) 2 , where 3-Clpy indicates 3-Chloropyridine. These two examples are the simplest cases of various onedimensional spin lattice models with clusters of spins interacting with Heisenberg interaction and interacting to each other only through Ising bonds, which have been investigated intensively during last decade [27][28][29][30][31][32][33][34][35][36][37] . Partition function and, thus, all thermodynamic functions for such models can be obtained analytically.…”